A college professor believes that students take an average of 15 credit hours per semester. A random sample of 24 students in his class of 250 reported the following number of credit hours that they were taking: 12,13,14,14,15,15,15,16,16,16,16,16,17,17,17,18,18,18,18,19,19,19,20,21 Does this sample indicate that students are taking more credit hours than the professor believes? BEFORE jumping to an answer, work through this problem using the following steps: 1) What are your null and alternative hypotheses? Answer verbally and with mathematical symbols. 2) One condition to check is that the data should be “Nearly normal”, or roughly unimodal and symmetric. Create a histogram or box plot of the data and assess this condition. 3) Is the sampling distribution of the mean a z or a student’s t statistic? Why? 4) Specify the decision rule using a = .05. 5) Sketch a normal curve graphic identifying the critical value and rejection area labeling the mean and the values. It is OK to draw this by hand and scan it into your document. 6) Calculate the test statistic using MegaStat. 7) Make the decision and state your conclusion in the context of this problem. 8) Regardless of its statistical significance, comment on the practical importance of the difference in credit load. 9) If this sample of students was extremely unusual and your conclusion was wrong (based on the entire population of students taking this professor’s classes), what type error would you be committing? Why? 10) Find a 95% confidence interval for the number of credit hours taken by the students in the professor’s class. Summarize what this interval means in one or two sentences.
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